We derive the analytical expression of the probability density of orbital angular momentum modes for elegant and standard Laguerre–Gaussian beams in turbulence. The results show that we can increase the initial topological charge of the beams to reduce the detrimental mode crosstalk induced by the turbulence. We also discuss the influence of the beam parameters on the probability of signal and the variances of crosstalk probability. The results obtained show that the beams with smaller beam width and longer wavelength have higher detection probabilities of signal and are less affected by turbulence. Comparing with the results of elegant and standard Laguerre–Gaussian beams, we find that elegant Laguerre–Gaussian beams display stronger turbulence resistance. Our results will be useful in free-space optical communications.

中文翻译：

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大气湍流中优雅与标准Laguerre-Gaussian光束螺旋光谱的比较研究

我们推导了湍流中优雅和标准Laguerre-Gaussian光束轨道角动量模式的概率密度的解析表达式。结果表明，我们可以增加光束的初始拓扑电荷，以减少湍流引起的有害模串扰。我们还讨论了光束参数对信号概率和串扰概率方差的影响。所得结果表明，光束宽度较小，波长较长的光束具有较高的信号检测概率，受湍流的影响较小。与优雅的和标准的Laguerre-Gaussian光束的结果进行比较，我们发现优雅的Laguerre-Gaussian光束显示出更强的抗湍流性。我们的结果将对自由空间光通信有用。